FDR is assassinated prior to assuming the Presidency on Feb. 15, 1933 by Zangara. Garner becomes president and serves ably but not is as unifying a figure as FDR (no fireside chat, a much leaner New Deal). After eight years, the people are in the mood for a change. Thomas Dewey wins the GOP nomination in 1940 with his youth and charisma (Wilkie has no reason to run without government competition stirring him up). Dewey wins against an uninspired and divided Democratic Party (Garner's term was a combative one). There, a 38 year old president.
As for his presidency, he would have taken the US into WWII. Military spending would have solved unemployment and saved the economy. He would have been combative towards Stalin and would have encouraged American forces to push east as fast as possible leading to a different division of Europe possibly capturing Berlin. A supporter of the UN, he also would have been tougher on Communism (the Nationalists are aided in their civil war either leading to victory or a north/south split averting the Korean War). The Communist Party may even be banned. He also would have likely expanded social programs and government regulation including Universal Healthcare. There is no 22nd Amendment. Dewey also would have supported Civil Rights infuriating the South; this, along with a demand for decolonization would hurt the Soviet's propaganda against the West. The US military would not be as large or as interventional without Korea revealing the faults of conventional forces following WWII; the US instead would be invested in air, naval, and nuclear forces.
The 1948 GOP primary would see Harold Stassen win. Claude Pepper wins the Democratic nomination. Animosity with the unions would hurt Pepper allowing a Stassen win who, at 41, would be the second youngest president.